Root Mean Square Error (RMSE)

A measure of the accuracy of spatial data, especially for assessing the fit of models or the precision of georeferencing (inferred from standard GIS usage).

Define the term Root Mean Square Error (RMSE)

A popular statistical metric for calculating the discrepancy between estimated or predicted values and actual observed values is the Root Mean Square Error, or RMSE. The main purpose of RMSE in GIS and remote sensing is to evaluate the precision of spatial data, such as the elevation or positional accuracy of georeferenced imagery.

Formula:

RMSE=1n∑i=1n(xi−yi)2\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n}(x_i - y_i)^2}RMSE=n1i=1∑n(xi−yi)2

xix_ixi = observed value
yiy_iyi = predicted or estimated value
nnn = number of observations

Key Points:

Higher accuracy is shown by a lower RMSE.
The same units as the original data are used to express it (e.g., meters for positional accuracy).
The variance and bias of errors are combined into a single metric by RMSE.

In GIS, for instance, RMSE indicates how closely the transformed image coordinates match the real GPS coordinates when a satellite picture is georeferenced using a set of GPS ground control points.

Related Keywords

By computing the square root of the average squared discrepancies between predicted and observed values, the Root Mean Square Error (RMSE) is a commonly used metric to assess a model's accuracy. It shows how closely predictions match actual results; higher model performance is indicated by lower RMSE values.

The Root Mean Square Error (RMSE) measures prediction accuracy and is given by:

RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}

Lower RMSE means better accuracy.

A popular metric in machine learning for calculating the discrepancy between expected and actual data is called root mean square error, or RMSE. Larger errors are given more weight when calculating the square root of the average of squared errors. Regression tasks and model performance comparison benefit from a decreased RMSE, which denotes improved model accuracy.

Regression models' prediction accuracy is assessed using two metrics: RMSE (Root Mean Squared Error) and MAE (Mean Absolute Error). MAE is simple to understand because it calculates the average magnitude of errors without taking into account their direction. Larger errors are penalized more severely by RMSE, which squares the errors prior to averaging and then takes the square root. Generally speaking, RMSE is more sensitive to outliers than MAE, which is more resilient.